To make the chia jam: Place all the ingredients, including any juice from the thawed blackberries, in a medium bowl. Crush the berries a little with a fork, and stir to mix, making sure all the chia seeds have been moistened with the juice from the berries. Cover and allow jam to thicken in the refrigerator for at least 6 hours. This can be made 2 weeks ahead and kept refrigerated..
Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
Brush each side of bread with olive oil and place on baking sheet.
Bake for 15 minutes, turning after 7 or 8 minutes. Set aside (can be stored in an airtight container for several days).
To assemble: spread a medium-thick layer of the chia jam on each piece of crostini and add a dollop of burrata cheese on top and flaky salt. Garnish with edible flowers, if desired.